In simple terms
A friendly intro before the formal notes — no formulas yet.
Damped and forced oscillations, resonance
Cambridge 9702 Paper 4 — Damped and forced oscillations, resonance (17.3). Senpai Corner diagram-backed pilot with premium structure and live visuals.
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17.3 Damped and forced oscillations, resonance.
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All oscillations eventually come to a stop due to resistive forces, such as friction or air resistance (drag).
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These resistive forces act on an oscillating system causing damping .
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Damping is defined as the reduction in energy and amplitude of oscillations due to resistive forces on the oscillating system .
What this topic covers
The official Cambridge syllabus points this lesson works through.
- 17.3.1
Understand that a resistive force acting on an oscillating system causes damping
- 17.3.2
Understand and use the terms light, critical and heavy damping and sketch displacement-time graphs illustrating these types of damping
- 17.3.3
Understand that resonance involves a maximum amplitude of oscillations and that this occurs when an oscillating system is forced to oscillate at its natural frequency
Explore the concept
Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.
Step-synced diagram — highlights what to look for in the simulation above.
Step 1
17.3 Damped and forced oscillations, resonance.
10 more simulations for this topic — run them in the Simulations section below
Simulations
Every simulation here runs the real model — try the steps on a card, then check what you see against the notes.
10 simulations · 4 to start with
Start herein this order — each one shows a different piece of the topic
- PhETStart here · 19702 17.3
Pendulum Lab
Add friction to a swinging pendulum and watch the amplitude decay cycle by cycle.
Why this one: Add friction and watch the amplitude decay cycle by cycle while the period stays almost unchanged.
Try this
- Set friction to a small value and swing — note how the amplitude falls while T stays the same.
- Raise friction to maximum — does the pendulum still oscillate, or just creep back?
- Open the energy graph and watch the thermal bar fill.
Look for Light damping: same period, amplitude decays exponentially; heavy damping: no oscillation.
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
- PhysicsHubStart here · 29702 17.1 · 9702 17.2 · 9702 17.3
Spring Mass System Simulator
Vertical mass on a spring; student sets bob mass, spring constant, damping, rest length and gravity and reads period/frequency and decay in real time
Why this one: Slide the damping from light to heavy and compare how quickly the oscillation dies.
Try this
- Set damping to zero and read the period.
- Double the bob mass and read it again.
- Add damping and watch the decay.
Look for Period grows with mass and falls with spring constant; damping shrinks the amplitude while leaving the period almost unchanged.
PhysicsHub (@mattqdev) · MIT
- PhETStart here · 39702 17.3
Masses and Springs
Damped spring oscillations — tune the damping slider and compare decay envelopes.
Why this one: Tune the damping slider and compare the decay envelopes of the same spring.
Try this
- Set damping to none and start a bounce — the amplitude never drops.
- Set damping to about a quarter — count how many cycles before the amplitude halves.
Look for The exponential envelope: each cycle loses the same fraction of its amplitude.
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
- SimuPhysicsStart here · 49702 17.3 · IB C.4 · IB C.1
Resonance in Harmonic Oscillator
Drive an oscillator at a frequency you choose and plot the amplitude response as you sweep through resonance
Why this one: Sweep the driving frequency and plot the amplitude response — the resonance curve peaks near f₀.
Try this
- Drive well below the natural frequency and read the amplitude.
- Sweep up to the natural frequency.
- Sweep past it and compare.
Look for Amplitude is greatest when the driving frequency equals the natural frequency.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
More simulations6 more on this topic — core ones first
- SimuPhysicsCore9702 8.1 · 9702 17.3 · IB C.4
Acoustic Resonance
A standing wave forms in an air column; change its length to hear and see the resonant frequency shift
Try this
- Set a length and read the resonant frequency.
- Double the length and compare.
- Find the node and antinode positions.
Look for A longer air column resonates at a lower frequency.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
- PhysicsHubCore9702 17.1 · 9702 17.2 · 9702 17.3
Simple Pendulum Simulation
Pendulum bob; set length, mass, gravity, damping and initial angle, read period and frequency, and push the amplitude to break the small-angle approximation
Try this
- Set a small initial angle and read the period.
- Double the length.
- Raise the initial angle towards 90° and read the period again.
Look for Period depends on length and g but not on mass, and grows beyond the small-angle value at large amplitude.
PhysicsHub (@mattqdev) · MIT
- PhysicsHubCore9702 17.1 · 9702 17.2 · 9702 6.2
Horizontal Spring
Mass on a frictionless horizontal surface tied to a wall by a spring; drag the mass to set amplitude and set mass, spring constant, damping and rest length
Try this
- Drag the mass out a small distance and release.
- Drag it twice as far.
- Double the spring constant.
Look for The period is independent of amplitude and falls as the spring constant rises.
PhysicsHub (@mattqdev) · MIT
- SimuPhysics9702 17.3 · 9702 21.1 · IB C.4
Wireless Radio Tuning
Several stations broadcast at once; tune the LC circuit and only the station matching its natural frequency comes through
Try this
- Tune the circuit to one station.
- Tune between stations and listen.
- Compare the station frequency with the circuit frequency.
Look for A station comes through when its frequency matches the circuit's natural frequency.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
- SimuPhysics9702 17.3 · IB C.1
Coupled Pendulum Simulation
Two identical pendulums are coupled and energy sloshes between them; find the two modes in which it does not
Try this
- Start one pendulum and watch the energy transfer.
- Start both in phase.
- Start both in antiphase.
Look for Energy transfers fully between the pendulums except in the in-phase and antiphase modes.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
- SimuPhysics9702 20.5 · 9702 17.3 · IB D.4
Pendulum Damped due to Eddy Currents
A solid metal plate swinging between magnet poles stops in a couple of swings while a slotted plate keeps going; switch plate types
Try this
- Swing the solid plate and count the swings.
- Switch to the slotted plate and count again.
- Watch the induced current loops in each.
Look for Eddy currents in the solid plate oppose its motion, and slots break those current loops.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
Full topic notes
Formal explanation with the rigour you need for the exam.
Damping: The Loss of Energy
Damping is essentially the process where energy is taken away from an oscillating system. This energy dissipation reduces the total mechanical energy, causing a gradual decrease in the maximum displacement, or amplitude, of the oscillations until the system eventually comes to rest. Damping forces always oppose the direction of motion, like air resistance or friction.
17.3 Damped and forced oscillations, resonance.
All oscillations eventually come to a stop due to resistive forces, such as friction or air resistance (drag).
These resistive forces act on an oscillating system causing damping .
Damping is defined as the reduction in energy and amplitude of oscillations due to resistive forces on the oscillating system .
Damping continues until the oscillator comes to rest at the equilibrium position.
Frequency does not change during damping only the amplitude of the oscillation decreases.
Free vs. Forced Oscillations
A system performing free oscillations moves only under the influence of its internal restorative forces, like a spring-mass system in a vacuum. It oscillates at its own unique natural frequency (f₀), which depends on its physical properties, such as mass and stiffness, without any external interference.
Forced oscillations, on the other hand, occur when an external, periodic driving force is continuously applied to a system. This force makes the system oscillate at the driving frequency (f_d) of the external force. Think of pushing a child on a swing – you are applying a periodic driving force.
Resonance: The Perfect Frequency Match
Resonance is a special case of forced oscillation that happens when the driving frequency of the external force exactly matches the natural frequency of the oscillating system (f_d = f₀). When this condition is met, there's incredibly efficient transfer of energy from the driving force to the system.
This efficient energy transfer causes a dramatic and significant increase in the amplitude of the oscillations. Even a small driving force can produce very large amplitudes if applied at the resonant frequency.
Useful Applications: Resonance is vital for tuning radio receivers, generating sound in musical instruments, and in MRI scanners.
Undesirable Effects: Can be destructive, such as bridges collapsing under resonant wind forces or excessive vibrations damaging machinery components.
The Damping-Resonance Relationship
Damping has a crucial role in controlling the effects of resonance. Without damping, theoretical resonance could lead to infinite amplitude, which isn't physically possible. In reality, damping limits the maximum amplitude achieved at resonance.
Peak Amplitude: Increasing damping significantly reduces the maximum amplitude reached at the resonant frequency.
Sharpness of Resonance: Higher damping makes the resonance curve broader and less 'sharp', meaning the amplitude doesn't drop off as quickly away from f₀.
Resonant Frequency Shift: Heavy damping can also cause a slight shift in the frequency at which the peak amplitude (resonance) occurs, typically to a slightly lower frequency.
Worked examples
See the formulas applied — reveal one step at a time, like the exam.
An oscillating system experiences resonance. Describe how its amplitude-driving frequency graph would change if the damping in the system was increased significantly.
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Reduced Peak Amplitude: The most noticeable change would be a substantial decrease in the maximum amplitude achieved at the resonant frequency. The peak of the curve would be much lower.
A mechanical oscillator of mass 0.50 kg is attached to a spring, giving it a natural frequency of 2.0 Hz. The system is lightly damped and is driven by a periodic force at its resonant frequency. The system reaches a steady-state amplitude of 5.0 cm. The damping force is given by F_d = -0.8v, where v is the velocity in m/s. Calculate the average power that must be supplied by the driving force to maintain this constant amplitude.
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Identify knowns and the goal:
How it all connects
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Glossary
Key terms for this topic — skim now; the Check step will test them.
- free oscillations
A system performing free oscillations moves only under the influence of its internal restorative forces, like a spring-mass system in a vacuum. It oscillates at its own unique natural frequency (f₀), which depends on its physical properties, such as mass and stiffness, without any external interference.
- natural frequency
It oscillates at its own unique natural frequency (f₀), which depends on its physical properties, such as mass and stiffness, without any external interference.
- Forced oscillations
Forced oscillations, on the other hand, occur when an external, periodic driving force is continuously applied to a system. This force makes the system oscillate at the driving frequency (f_d) of the external force.
- driving frequency
This force makes the system oscillate at the driving frequency (f_d) of the external force.
- Resonance
Resonance is a special case of forced oscillation that happens when the driving frequency of the external force exactly matches the natural frequency of the oscillating system (f_d = f₀).
Quick check
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Teach it back
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Teach it back
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Revision flashcards
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Key takeaways
Review these before you close the topic — retrieval beats re-reading.
17.3 Damped and forced oscillations, resonance.
All oscillations eventually come to a stop due to resistive forces, such as friction or air resistance (drag).
These resistive forces act on an oscillating system causing damping .
Damping is defined as the reduction in energy and amplitude of oscillations due to resistive forces on the oscillating system .
Damping continues until the oscillator comes to rest at the equilibrium position.
Frequency does not change during damping only the amplitude of the oscillation decreases.
Practice — then mark it
The whole point: a real Cambridge question, marked mark-by-mark.
State what is meant by resonance.
Explain the decrease with time of the amplitude of the oscillations of the ball.
Extra simulations & links
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Frequently asked
Checkpoint
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